How to do it...

In order to find the partners, you need to perform the following steps:

1. Get an empty recordset for res.partner:

    @api.model 
    def find_partners_and_contacts(self, name): 
        partner = self.env['res.partner'] 

2. Write the search domain for your criteria:

     domain = ['|',  
              '&',  
               ('is_company', '=', True), 
               ('name', 'like', name), 
               '&', 
               ('is_company', '=', False), 
               ('parent_id.name', 'like', name) 
               ] 

3. Call the search() method with the domain and return the recordset:

    return partner.search(domain)