Q: An ex left me their dog and cat almost 5 years ago, now they are threatening to come take them back. Can that happen?

A: Your argument is either (1) they were a gift to you, and once given, title passes to the recipient, so those pets are yours now; or (2) he abandoned them--abandonment being the intentional relinquishment of property (pets are property under Maryland law) and giving up of rights, which may be proven by acts consistent with such intent or inconsistent with maintaining a right of ownership, such as leaving property for a long period of time and never exercising rights over it or expressing an intention to maintain ownership. I assume you have purchased food, housed, exercised, tended to and paid veterinarian bills for these pets over 5 years with no assistance from your ex. The amounts you have expended over this time in food alone would exceed the fair market value of the animals.

Gift or abandonment would not apply if, at the start of your keeping the animals, there was an agreement that you would care for them until your ex returned to retrieve them, and the two of you maintained this arrangement over those five years with the continuing understanding that your ex claimed the pets as his and would one day return to get them back. You could have ended that arrangement (if it existed) at any time by declaring you no longer agreed to care for them for his benefit, and he had to remove them within 30 days or they would be deemed abandoned. Regardless, in such a scenario, you may be entitled to claim your reasonable expenditures incurred to maintain and care for the pets.

If you fear he will come in person to your property, and you do not want that, you need to send him, in writing (email is fine), notice that he may not come onto your property, and if he does so without your express permission (and nobody else's permission) that he will be deemed to be trespassing and you will call the police and have him charged. Keep a printed copy of that notice--you will need it to show the police if he ever trespasses on your property. You do not describe sufficient facts to justify the issuance of a peace order.