No, you don't lose all rights just because you leave the home. This is a common myth. If things are escalating, and the situation in the home is volatile and potentially dangerous, you need to protect yourself.
Do, however, seek legal advice as soon as possible, in order to protect your rights, make arrangements for any children and avoid any confusion about your intentions. You also cannot claim certain rights, such as the right to an equalization payment, after a certain number of years following separation or divorce.
If you have left children behind, it is especially important to act quickly, to ensure that your relationship with them remains intact. If you are their primary caregiver, you should make all efforts to have the children come with you when the leave the home. You will need to take immediate steps to agree upon a parenting schedule with the other parent, or to obtain a court order for custody and access.
If the situation in the home is fairly stable, though, it often makes sense to wait until there is a Separation Agreement or court order in place. That way, the transition will be smoother for the children, and it will be easier to buy or rent a new home if you know what the child support, spousal support and property arrangements will be. You may need to show the bank or landlord your Separation Agreement or court order, to prove your income.