In US it's about the same but ex husband likely will also pay an alimony on top of that (besides child support). What this example shows, there is no (and IMHO cannot be) an objective standard for this identify thing whatsoever, therefore it will be and already is exploited a lot if it gives an advantage of some sort.
Thankfully not all states have alimony, it is an anachronism from back in the days when women didn't own property, didn't have careers and were pretty much screwed if they got divorced. Today a woman can leave a man for any reason, walk off with half his assets and his kids, collect child support, and then in alimony states he's stuck paying a large fraction of his paycheck to his ex wife even if she is settled in with a new guy. Even though my state does not have alimony, marriage has long struck me as an incredibly large risk relative to the reward, with around 50% of marriages ending in divorce it is playing Russian roulette with half of the chambers loaded.
In some countries you can be considered 'married' if you live together long enough but are never legally married.
What if my sister were to divorce and she and the children ended up living with me? Surly that wouldn't apply.

I'd be curious to know which countries it is exactly. I've never heard of that and it sure sounds dodgy. But if it's true, the claim should be backed up with some evidence.
Legally speaking, there are circumstances in which an explicit contract between two persons may not be required to establish an implicit contract. That is for instance the case for house renting, at least over here. If no renting contract was established, but someone is effectively living in a house and paying a rent monthly to a landlord, then after some given delay (don't remember how long), it's considered there's an implicit contract. I've never heard of such a thing for something as private and personal as marriage, and would be curious to know where it would apply. If it ever exists, I would suspect this would be in some country that is politically led by an official religion. From a civil point of view, an implicit marriage sounds like a complete nonsense.
In the UK common-law marriage hasn't technically been a thing since 1753, but people cohabiting sometimes get thought of as beeing in a common-law marriage. Common-law marriage was basically 2 people agreed to live as if they were married, but without the ceremony.
Depending on how you're cohabiting you might have certain protections/responsibilities e.g. if you're helping to maintain the house etc. Over the past decade or so, they've been talking about adding additional protections to those cohabiting since it has increased in popularity.
There are examples of where an implicit marriage makes sense; 2 people living together for 50 years - one falls ill, all of their relatives are dead, who is the next of kin?
Or the classic whereby a couple have a child, the woman leaves her job to raise the child in her partner's house, then the man meets a new girlfriend and runs off with her. Here an implicit marriage would give the woman certain financial protections such as not becoming homeless; the alternative is she has no recourse.
It does serve a purpose.
The logic of it applying it implicitly goes a bit like this; well they're living together, they're in a intimate relationship, they argue, they go on holiday together, they share the bills - these are all things married couples do - and they've being doing it for a significant period of time, so we might as well treat them as married. I'm sure you've met people who live in this kind of situation - for all intents and purposes they are effectively married; whether in the official sense or not; so why should they be treated differently in the legal sense.
Obviously in practice they are treated differently - but that isn't really just