The third quality of surrender is ananyagatitvam, meaning exclusiveness or singular devotion. Earlier we talked about saralata and akinchanatvam. A symptom of surrender is to proclaim loyalty to one master. Lord Hanuman is a classic example of this. He was undeterred in His service to His master Lord Ramachandra.
I heard this story but cannot recall the exact Puranic source. The story goes something like this that illustrates Lord Hanuman's singular devotion. Once, Lord Krishna had an audience with the eternal traveling spaceman Sage Narada. During their conversation, Lord Krishna requested Narada to seek audience with Lord Hanuman. Narada muni immediately traveled to the caves where Lord Hanuman is eternally reciting Ramayan. Narada meets Hanumanji and conveys the message Krishna would like to meet Him. Hanumanji replied that He is busy studying Ramayana. Once He is done, He will come. Narada muni was besides himself. He traveled to Dwaraka and conveyed the message to Krishna. Krishna smilingly acknowledged the expected response. Krishna knew Hanumanji will not come. Then again, Krishna said "this time tell that Lord Ram wants to see Him". So Narada went back to the cave where Hanumanji was meditating and again conveyed the message. Hearing that Lord Rama is awaiting His audience, immediately just as He jumped to Lanka, He jumped to Dwaraka and there His beloved Lord Ramachandra was standing to see Him. Hanumanji immediately prostrated and paid His dandavat pranams. Krishna manifested Himself as Rama and gave darshan to Hanumanji just to please Hanumanji.
The story goes to show how Lord Hanuman was so focused and fixed on His devotion to Lord Rama that even Krishna is not His object of service. Although there is no difference between Rama and Krishna, still the inner mood of seva and love can and should be expressed only to the master one is loyal to. Lord Hanuman was loyal and His unconditional love was only to His eternal master Lord Rama. Likewise, the Lord also is singularly attached to His devotee in the mood He reciprocates. Such is the kindness and love of Krishna or in this case Rama.
From this story, we can learn that in order to surrender (saranagati), one has to be loyal to His master despite all obstacles and constantly meditate on His beloved master as his life and soul. Therefore, ananyagatitvam or singular devotion is a significant symptom of surrender or saranagati.